DOA Estimation Using Compressive Sensing Based on DFT Measurement Matrix

In this paper, a new method is proposed to estimate the direction of arrival (DOA) using non-uniform linear array structure and modeling the measurement matrix as a DFT matrix. In order to estimate the DOA using compressive sensing (CS), continuous angle space should be divided into a discrete set using small steps. This division, leads to the increment of mutual coherence between columns of the measurement matrix and performance of the sparse recovery algorithms is degraded. To solve this problem, we propose a new method in which DFT matrix with mutual coherence of zero is used as the measurement matrix. In order to increase the accuracy of estimation, the size of DFT matrix or the number of antennas should be increased. Implementation of an array with large number of antennas is complex and expensive. A solution to decrease the number of antennas is using a non-uniform linear array and constructing a virtual uniform linear array. A virtual uniform linear array can be constructed by vectorizing the correlation matrix of the received signal of a non-uniform linear array. Increasing the number of antennas in the virtual array will increase the size of DFT matrix. Therefore, the accuracy of DOA estimation will be increased. Simulation results show that DOA estimation using compressive sensing, based on DFT measurement matrix, has a good performance in terms of mean square error of estimation.